Question

A long straight wire lies on a horizontal table and carries a current of 0.48 μA. A proton with charge qp = 1.60218 × 10^−19 C and mass mp = 1.6726 × 10^−27 kg moves parallel to the wire (opposite the current) with a constant velocity of 12200 m/s at a distance d above the wire. The acceleration of gravity is 9.8 m/s^2.

Determine this distance of d. You may ignore the magnetic field due to the Earth.

Answer in units of cm.

Answer 1

Magnetic force on the proton due to the current wire is

are the unit vectors along positive X( right), positive Y( up) and positive Z ( out of the plane) respectively.

The current in the wire is towards right (say) along positive X direction, then magnetic field at proton due to current wire is

As the proton is moving in opposite direction to current,

Where

That is direction of magnetic force on the proton is upwards .

Gravitational force on proton is

Net force on proton is zero,